Andy and Vanessa has some money each. If Vanessa gives Andy $12, he will have 5 times as much money as her. If Andy gives Vanessa $16, he will have the same amount of money as her. How much money does each person have respectively?
- Andy?
- Vanessa?
| |
Case 1 |
Case 2 |
| |
Andy |
Vanessa |
Andy |
Vanessa |
| Before |
5 u - 12 |
1 u + 12 |
3 u + 16 |
3 u - 16 |
| Change |
+ 12 |
- 12 |
- 16 |
+ 16 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Vanessa gives Andy some money or Andy gives Vanessa some money, the total amount of money remains the same.
Total amount that Andy and Vanessa have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Andy and Vanessa each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Andy has at first in Case 1 and Case 2 is the same.
5 u - 12 = 3 u + 16
5 u - 3 u = 16 + 12
1 u = 28
Amount that Andy has
= 3 u + 16
= 3 x 28 + 16
= 84 + 16
= $100
(b)
Amount that Vanessa has
= 1 u + 12
= 28 + 12
= $40
Answer(s): (a) $100; (b) $40
